Exploring the ELI Measure

Exploring the ELI

eli_data <- clean_data_eli %>% 
  select(sub_id, eli_number, eli_targ_pmc, eli_self_pmc, itt_comp_gmc,
         target_condition, eli_targ, eli_self, eli_stereo, eli_stereo_pmc,
         analog_condition, itt_comp) %>% 
  unique() %>% 
  na.omit() 

eli5_data <- clean_data_eli %>% 
  filter(eli_number %in% c("1", "2", "3", "4", "5")) %>% 
  select(sub_id, eli_number, eli_targ_pmc, eli_self_pmc, itt_comp_gmc,
         target_condition, eli_targ, eli_self, eli_stereo, eli_stereo_pmc,
         analog_condition, itt_comp) %>% 
  unique() %>% 
  na.omit() 

eli_wide_self <- clean_data_eli %>% 
  select(sub_id, eli_number, eli_self, pol_orient_1, pol_orient_2, pol_orient_3) %>% 
  unique() %>% 
  pivot_wider(names_from = eli_number, values_from = eli_self) %>% 
  rename("Politics: Overall" = pol_orient_1,
         "Politics: Social" = pol_orient_2,
         "Politics: Economic" = pol_orient_3,
         "ElI 1" = `1`,
         "ElI 2" = `2`,
         "ElI 3" = `3`,
         "ElI 4" = `4`,
         "ElI 5" = `5`,
         "ElI 6" = `6`,
         "ElI 7" = `7`,
         "ElI 8" = `8`,
         "ElI 9" = `9`,
         "ElI 10" = `10`)

# These look the same as in the PSPB paper
hist(eli_wide_self$`ElI 1`)

hist(eli_wide_self$`ElI 2`)

hist(eli_wide_self$`ElI 3`)

hist(eli_wide_self$`ElI 4`)

hist(eli_wide_self$`ElI 5`)

Exploring relationship of ELI vars with each other and political orientation

Self

eli_self_cor <- eli_wide_self %>% 
  select(-sub_id)

eli_pol_cor <- cor(eli_self_cor)

corrplot(eli_pol_cor, 
         is.corr = TRUE, 
         #method = "number", 
         method = 'color',
         tl.cex = .85,
         tl.col = 'black',
         addgrid.col = 'white',
         addCoef.col = 'grey50')

Responses on the ELI are not related to responses on the political orientation questions nor each other (aka orthogonal)

Target

eli_wide_targ <- clean_data_eli %>% 
  select(sub_id, eli_number, eli_targ, pol_orient_1, pol_orient_2, pol_orient_3) %>% 
  unique() %>% 
  pivot_wider(names_from = eli_number, values_from = eli_targ) %>% 
  select(-sub_id) %>% 
   rename("Politics: Overall" = pol_orient_1,
         "Politics: Social" = pol_orient_2,
         "Politics: Economic" = pol_orient_3,
         "ElI 1" = `1`,
         "ElI 2" = `2`,
         "ElI 3" = `3`,
         "ElI 4" = `4`,
         "ElI 5" = `5`,
         "ElI 6" = `6`,
         "ElI 7" = `7`,
         "ElI 8" = `8`,
         "ElI 9" = `9`,
         "ElI 10" = `10`)

eli_targ_matrix_targ <- cor(eli_wide_targ)

corrplot(eli_targ_matrix_targ, 
         is.corr = TRUE, 
         #method = "number", 
         method = 'color',
         tl.cex = .85,
         tl.col = 'black',
         addgrid.col = 'white',
         addCoef.col = 'grey50')

The target has slightly higher correlations overall for the ELI, but lower ones in relation to political orientation

Stereo

eli_wide_stereo <- clean_data_eli %>% 
  select(sub_id, eli_number, eli_stereo, pol_orient_1, pol_orient_2, pol_orient_3) %>% 
  unique() %>% 
  pivot_wider(names_from = eli_number, values_from = eli_stereo) %>% 
     rename("Politics: Overall" = pol_orient_1,
         "Politics: Social" = pol_orient_2,
         "Politics: Economic" = pol_orient_3,
         "ElI 1" = `1`,
         "ElI 2" = `2`,
         "ElI 3" = `3`,
         "ElI 4" = `4`,
         "ElI 5" = `5`,
         "ElI 6" = `6`,
         "ElI 7" = `7`,
         "ElI 8" = `8`,
         "ElI 9" = `9`,
         "ElI 10" = `10`) %>% 
    select(-sub_id)

eli_stereo_matrix_stereo <- cor(eli_wide_stereo)

corrplot(eli_stereo_matrix_stereo, 
         is.corr = TRUE, 
         #method = "number", 
         method = 'color',
         tl.cex = .85,
         tl.col = 'black',
         addgrid.col = 'white',
         addCoef.col = 'grey50')

Again, higher correlations than for the self, but still only .35 as the highest. Low correlations with politics, but higher than with the target.

Exploring variance in intercepts for ELI

https://bbolker.github.io/mixedmodels-misc/glmmFAQ.html

Random intercept

With self

eli_randint_test <- lmer(eli_targ_pmc ~ eli_self_pmc + # itt does not work as a RE; model does not converge
                     (1 | sub_id), 
                   data = eli_data) # Same as above, works with clean_data but not the smaller df specific to this analysis

summary(eli_randint_test)

## Linear mixed model fit by REML ['lmerMod']
## Formula: eli_targ_pmc ~ eli_self_pmc + (1 | sub_id)
##    Data: eli_data
## 
## REML criterion at convergence: 12331.4
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.0103 -0.5900  0.0054  0.6712  3.4945 
## 
## Random effects:
##  Groups   Name        Variance                             
##  sub_id   (Intercept) 0.00000000000000000000000000000001469
##  Residual             1.07012291677120230382058707618853077
##  Std.Dev.             
##  0.0000000000000001212
##  1.0344674556365716089
## Number of obs: 4240, groups:  sub_id, 424
## 
## Fixed effects:
##                             Estimate              Std. Error t value
## (Intercept)  0.000000000000000006571 0.015886707663029700499   0.000
## eli_self_pmc 0.009365790070278842347 0.012313692726427382870   0.761
## 
## Correlation of Fixed Effects:
##             (Intr)
## eli_slf_pmc 0.000 
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')

The random variance for the intercept is 0, which is causing the singularity. This does not occur with the BFI. The data looks normal in the descriptives document. Checking some more stuff below.

Checking individual intercepts/slopes

Person mean centered variables

eli_coeffs_per_sub_c  <- lmList(eli_targ_pmc ~ 1 + eli_self_pmc | sub_id, eli_data)
eli_coeffs_per_sub_c

## Call:
##   Model: eli_targ_pmc ~ 1 + eli_self_pmc | sub_id 
##    Data: eli_data 
## 
## Coefficients:
##                                    (Intercept)               eli_self_pmc
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## 510  0.000000000000000163548142946119606198672  0.06832298136645958974711
## 512 -0.000000000000000113292853063999917407328  0.02836879432624114100170
## 515  0.000000000000000200619055347240045339990  0.14285714285714287696827
## 517  0.000000000000000030528986683275656125967  0.10869565217391304046135
## 520 -0.000000000000000308405784051577171570610  0.33027522935779823898272
## 523 -0.000000000000000018004274197829233732029  0.12820512820512819374130
## 527  0.000000000000000247358584574720302098575 -0.13259668508287292265635
## 530 -0.000000000000000147542051138120026703850  0.14049586776859507297743
## 536 -0.000000000000000050712038990552334180261 -0.51388888888888895056795
## 540  0.000000000000000211682606193595231786403 -0.25490196078431381909724
## 
## Degrees of freedom: 4240 total; 3392 residual
## Residual standard error: 1.05803

Uncentered variables

eli_coeffs_per_sub  <- lmList(eli_targ ~ 1 + eli_self | sub_id, eli_data)
eli_coeffs_per_sub

## Call:
##   Model: eli_targ ~ 1 + eli_self | sub_id 
##    Data: eli_data 
## 
## Coefficients:
##                   (Intercept)                    eli_self
## 1    4.0677966101694913447773 -0.271186440677966267287502
## 2    2.3281250000000000000000  0.132812499999999916733273
## 3    3.3214285714285707307170 -0.035714285714285698425385
## 4    2.7434944237918204024140  0.308550185873606108710732
## 5    2.7272727272727270708685  0.204545454545454530315141
## 6    2.2096069868995620311125  0.222707423580785879302368
## 8    4.8196721311475414495362 -0.491803278688524636574897
## 10   3.5692307692307680966337 -0.076923076923076788569134
## 11   1.0000000000000013322676  0.749999999999999777955395
## 12   2.7999999999999984900967  0.000000000000000219427092
## 13   3.0000000000000004440892  0.125000000000000083266727
## 14   3.5100671140939598835473 -0.026845637583892714012057
## 15   4.2483221476510060199416 -0.328859060402684477697477
## 16   2.0567375886524805750355  0.390070921985815610710802
## 17   2.9999999999999991118216  0.000000000000000052012348
## 19   4.1874999999999991118216 -0.562500000000000222044605
## 20   2.6714285714285712636240  0.142857142857142876968268
## 21   2.9999999999999960031971  0.000000000000000672553716
## 22   2.9999999999999991118216 -0.000000000000000024212645
## 23   2.9999999999999991118216  0.000000000000000000000000
## 25   4.1923076923076916244781 -0.192307692307692262856378
## 26   3.5140845070422530582732 -0.239436619718309706694725
## 27   3.6763485477178421412248 -0.265560165975103679159020
## 29   3.2173913043478266082786  0.072463768115941920577860
## 30   0.6938775510204090446464  0.693877551020408045445720
## 32   2.9999999999999991118216 -0.000000000000000084825507
## 33   3.8837209302325574888926 -0.124031007751938024408211
## 34   3.8993288590604020527053 -0.281879194630872520477283
## 35   3.4617940199335550666149 -0.109634551495016580036079
## 36   3.6666666666666674068153 -0.190476190476190937461709
## 37   3.1020408163265313916668  0.030612244897959023370859
## 38   2.8859060402684550972197  0.073825503355704688579486
## 39   2.9285714285714274929262  0.132653061224489832170548
## 40   2.2758620689655177926625  0.206896551724137872652065
## 41   2.1562500000000000000000  0.218749999999999861222122
## 42   2.7377049180327852617722  0.049180327868852811989964
## 43   2.9090909090909091716526  0.053030303030303080347174
## 44   4.1203703703703693506100 -0.268518518518518378712656
## 45   5.7352941176470570994184 -0.705882352941176405280999
## 47   2.6716417910447765038384  0.084577114427860630718747
## 48   6.3827160493827150844481 -1.049382716049382935352696
## 50   2.5394736842105261054314  0.223684210526315735423353
## 51   3.4343891402714921134987 -0.040723981900452434212756
## 52   3.6666666666666674068153 -0.083333333333333453607494
## 53   3.4074074074074069962137 -0.064814814814814949994748
## 54   4.8852459016393439128478 -0.508196721311475418936254
## 55   3.8374999999999972466469 -0.312499999999999777955395
## 58   2.4888888888888902606311  0.088888888888888711869996
## 59   2.9153439153439153486147 -0.005291005291005274231708
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## 397  2.7639751552795019939879  0.161490683229813553056786
## 398  2.7583643122676577696950  0.174721189591078074343500
## 399 -0.0769230769230762889688  0.846153846153846145305977
## 400  2.7473309608540921189501  0.046263345195729617398417
## 401  2.7639751552795028821663  0.161490683229813636323513
## 402  2.0833333333333339254523  0.208333333333333092785011
## 404  9.0000000000000124344979 -1.250000000000002664535259
## 405  2.8552036199095018886851  0.013574660633484208344113
## 406  3.6376811594202886901428  0.050724637681159430446787
## 407  4.8846153846153850253131 -0.282051282051282048435326
## 408  1.1538461538461548538947  0.627218934911242365082273
## 409  5.3538461538461534772182 -0.615384615384615307753791
## 411  5.1999999999999975131004 -0.499999999999999611421941
## 412  4.2500000000000008881784 -0.416666666666666629659233
## 413  1.5106382978723404963972  0.510638297872340385374912
## 414  0.8589743589743582541374  0.589743589743589979867977
## 415  4.1381215469613259472226 -0.226519337016574701104688
## 416  2.4807692307692308375522  0.211538461538461536326494
## 417  2.0000000000000004440892  0.333333333333333314829616
## 418  2.8529411764705887577520  0.058823529411764649554861
## 419  3.8066914498141266598452 -0.260223048327137662649733
## 420  4.0869565217391299327687 -0.163043478260869567630920
## 421  3.0243902439024372696963 -0.036585365853658353973987
## 423  2.4431818181818170110375 -0.011363636363635949352857
## 425  2.8571428571428558740308  0.142857142857142932479420
## 426  4.8474576271186426978943 -0.644067796610169440718607
## 427  3.3999999999999994670929  0.050000000000000002775558
## 428  3.3076923076923065991650  0.023668639053254360987699
## 429  1.7903225806451612545089  0.419354838709677435470979
## 430  2.9545454545454541417371  0.170454545454545386418133
## 431  3.3055555555555549140934 -0.027777777777777849094187
## 432  2.6335403726708066507456  0.180124223602484395678758
## 433  3.8852459016393434687586 -0.172131147540983575616735
## 435  5.2112676056338029795256 -0.591549295774647876378083
## 436  2.7318840579710146343473 -0.072463768115942031600163
## 437  3.8333333333333330372739 -0.274509803921568540374665
## 438  4.4999999999999982236432 -0.277777777777777568068984
## 440  3.9357429718875502899778 -0.184738955823293277136443
## 441  3.6511627906976737989453 -0.038759689922480515533731
## 442  1.5454545454545458582629  0.579545454545454363781687
## 443  2.4796380090497733839072  0.221719457013574761106156
## 445  2.4571428571428568510271  0.285714285714285420869629
## 446  3.9999999999999995559108  0.000000000000000012906081
## 447  4.7846153846153844924061 -0.538461538461538435917930
## 448  3.1162790697674416229290  0.124031007751937982774848
## 449  3.0698689956331874917339 -0.196506550218340486635427
## 450  3.6937799043062198300902 -0.320574162679425900268626
## 451  0.9405405405405404817287  0.702702702702702963755144
## 452  4.0185185185185181566681 -0.435185185185185119394191
## 453  2.4999999999999995559108  0.235294117647058736997323
## 454  1.6285714285714276705619  0.591836734693877764001968
## 455  4.4658385093167689561255 -0.322981366459627328158177
## 456  2.9999999999999991118216 -0.000000000000000060473687
## 457  2.0737704918032782153148  0.163934426229508156680481
## 459  4.4999999999999991118216 -0.599999999999999977795540
## 460  0.8225806451612905911830  0.758064516129032139879484
## 461  1.9999999999999991118216  0.294117647058823594719001
## 462  4.6842105263157893801917 -0.526315789473684625399130
## 463  2.9545454545454550299155 -0.189393939393939392257238
## 464  4.4673913043478261641894 -0.402173913043478492568283
## 474  3.0571428571428564957557  0.214285714285714412596917
## 476  2.6538461538461537436717  0.096153846153846117550401
## 481  2.1000000000000000888178  0.249999999999999916733273
## 482  3.3057851239669422405143 -0.082644628099173611524009
## 483  4.6243093922651929972290 -0.303867403314917128298589
## 489  2.2318840579710137461689  0.202898550724637277697937
## 498  3.4054054054054048172873  0.027027027027027018118988
## 501  3.3521594684385385143344 -0.076411960132890408003981
## 508  3.7195121951219514144782 -0.060975609756097469416058
## 510  3.0745341614906820382203  0.068322981366459645258260
## 512  3.1063829787234040757937  0.028368794326241151410040
## 515  2.7999999999999993782751  0.142857142857142627168088
## 517  2.7173913043478261641894  0.108695652173912846172321
## 520  2.3119266055045870622564  0.330275229357798238982724
## 523  2.6410256410256409687065  0.128205128205128249252454
## 527  4.2375690607734801673701 -0.132596685082872922656350
## 530  2.6363636363636366866103  0.140495867768595072977433
## 536  5.3472222222222214327303 -0.513888888888888950567946
## 540  4.1666666666666660745477 -0.254901960784313763586084
## 
## Degrees of freedom: 4240 total; 3392 residual
## Residual standard error: 1.05803

There seems to be variability in the intercepts, even though lmer is not finding it.

Scatterplot of variables

ggplot(clean_data_eli, aes(eli_self_pmc, eli_targ_pmc)) +
  geom_point()

Random intercept only

eli_randint_only <- lmer(eli_targ_pmc ~ 1 + # itt does not work as a RE; model does not converge
                     (1 | sub_id), 
                   data = eli_data) # Same as above, works with clean_data but not the smaller df specific to this analysis

summary(eli_randint_only)

## Linear mixed model fit by REML ['lmerMod']
## Formula: eli_targ_pmc ~ 1 + (1 | sub_id)
##    Data: eli_data
## 
## REML criterion at convergence: 12325
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.9969 -0.5800  0.0000  0.6767  3.4802 
## 
## Random effects:
##  Groups   Name        Variance                             
##  sub_id   (Intercept) 0.00000000000000000000000000000001469
##  Residual             1.07001651332861880128177745064022020
##  Std.Dev.             
##  0.0000000000000001212
##  1.0344160252667293776
## Number of obs: 4240, groups:  sub_id, 424
## 
## Fixed effects:
##                            Estimate              Std. Error t value
## (Intercept) 0.000000000000000006703 0.015885917827403422953       0
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')

With only first five ELI items

These were the ones used in the PSPB paper

eli5_randint_test <- lmer(eli_targ_pmc ~ eli_self_pmc + # itt does not work as a RE; model does not converge
                     (1 | sub_id), 
                   data = eli5_data) # Same as above, works with clean_data but not the smaller df specific to this analysis

summary(eli5_randint_test)

## Linear mixed model fit by REML ['lmerMod']
## Formula: eli_targ_pmc ~ eli_self_pmc + (1 | sub_id)
##    Data: eli5_data
## 
## REML criterion at convergence: 5708.1
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.2955 -0.4688 -0.0294  0.6000  3.5763 
## 
## Random effects:
##  Groups   Name        Variance Std.Dev.
##  sub_id   (Intercept) 0.0000   0.0000  
##  Residual             0.8605   0.9276  
## Number of obs: 2120, groups:  sub_id, 424
## 
## Fixed effects:
##              Estimate Std. Error t value
## (Intercept)   0.25528    0.02017   12.65
## eli_self_pmc -0.01700    0.01650   -1.03
## 
## Correlation of Fixed Effects:
##             (Intr)
## eli_slf_pmc -0.050
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')

Random Slopes/No random intercept

eli_randslopes_test <- lmer(eli_targ_pmc ~ eli_self_pmc + # itt does not work as a RE; model does not converge
                     (0 + eli_self_pmc | sub_id), 
                   data = eli_data) 


summary(eli_randslopes_test)

## Linear mixed model fit by REML ['lmerMod']
## Formula: eli_targ_pmc ~ eli_self_pmc + (0 + eli_self_pmc | sub_id)
##    Data: eli_data
## 
## REML criterion at convergence: 12253.9
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.0943 -0.5982  0.0068  0.6452  3.2360 
## 
## Random effects:
##  Groups   Name         Variance Std.Dev.
##  sub_id   eli_self_pmc 0.04537  0.2130  
##  Residual              0.99461  0.9973  
## Number of obs: 4240, groups:  sub_id, 424
## 
## Fixed effects:
##                             Estimate              Std. Error t value
## (Intercept)  0.000000000000000005827 0.015315897842633369522   0.000
## eli_self_pmc 0.012234199608380517260 0.016068790172722027115   0.761
## 
## Correlation of Fixed Effects:
##             (Intr)
## eli_slf_pmc 0.000

Running without the random intercept fixes the issue

Additional ELI analyses

Threat composite

comp_eli_randslopes <- lmer(eli_targ_pmc ~ eli_self_pmc*itt_comp_gmc + # itt does not work as a RE; model does not converge
                     (0 + eli_self_pmc | sub_id), 
                   data = eli_data) # Same as above, works with clean_data but not the smaller df specific to this analysis


summary(comp_eli_randslopes)

## Linear mixed model fit by REML ['lmerMod']
## Formula: eli_targ_pmc ~ eli_self_pmc * itt_comp_gmc + (0 + eli_self_pmc |  
##     sub_id)
##    Data: eli_data
## 
## REML criterion at convergence: 12233
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.2229 -0.6049  0.0141  0.6519  3.1456 
## 
## Random effects:
##  Groups   Name         Variance Std.Dev.
##  sub_id   eli_self_pmc 0.03695  0.1922  
##  Residual              0.99503  0.9975  
## Number of obs: 4240, groups:  sub_id, 424
## 
## Fixed effects:
##                                          Estimate              Std. Error
## (Intercept)                0.00000000000000000569  0.01531913279267939354
## eli_self_pmc               0.01357934379323691258  0.01540005841078596720
## itt_comp_gmc               0.00000000000000001164  0.01430741929851506340
## eli_self_pmc:itt_comp_gmc -0.08568263438990457448  0.01433422509918278950
##                           t value
## (Intercept)                 0.000
## eli_self_pmc                0.882
## itt_comp_gmc                0.000
## eli_self_pmc:itt_comp_gmc  -5.977
## 
## Correlation of Fixed Effects:
##             (Intr) el_sl_ itt_c_
## eli_slf_pmc  0.000              
## itt_cmp_gmc  0.000  0.000       
## el_slf_p:__  0.000 -0.017  0.000

tab_model(comp_eli_randslopes,
          digits = 3)

	eli_targ_pmc
Predictors	Estimates	CI	p
(Intercept)	0.000	-0.030 – 0.030	1.000
eli self pmc	0.014	-0.017 – 0.044	0.378
itt comp gmc	0.000	-0.028 – 0.028	1.000
eli self pmc * itt comp gmc	-0.086	-0.114 – -0.058	<0.001
Random Effects
σ2	1.00
τ00
τ00
τ11 sub_id.eli_self_pmc	0.04
ρ01
ρ01
ICC	0.06
N sub_id	424
Observations	4240
Marginal R2 / Conditional R2	0.013 / 0.071

Simple slopes

threat_levels = list(itt_comp_gmc = c(-1.07, 0.0, 1.07))
comp_simpslopes_eli <- emtrends(comp_eli_randslopes, ~ itt_comp_gmc,
                              var ="eli_self_pmc",
                              at = threat_levels)

comp_simpslopes_eli 

##  itt_comp_gmc eli_self_pmc.trend     SE  df asymp.LCL asymp.UCL
##         -1.07             0.1053 0.0219 Inf    0.0623    0.1482
##          0.00             0.0136 0.0154 Inf   -0.0166    0.0438
##          1.07            -0.0781 0.0215 Inf   -0.1203   -0.0359
## 
## Degrees-of-freedom method: asymptotic 
## Confidence level used: 0.95

test(comp_simpslopes_eli)

##  itt_comp_gmc eli_self_pmc.trend     SE  df z.ratio p.value
##         -1.07             0.1053 0.0219 Inf   4.802  <.0001
##          0.00             0.0136 0.0154 Inf   0.882  0.3779
##          1.07            -0.0781 0.0215 Inf  -3.624  0.0003
## 
## Degrees-of-freedom method: asymptotic

pairs(comp_simpslopes_eli)

##  contrast       estimate     SE  df z.ratio p.value
##  (-1.07) - 0      0.0917 0.0153 Inf   5.977  <.0001
##  (-1.07) - 1.07   0.1834 0.0307 Inf   5.977  <.0001
##  0 - 1.07         0.0917 0.0153 Inf   5.977  <.0001
## 
## Degrees-of-freedom method: asymptotic 
## P value adjustment: tukey method for comparing a family of 3 estimates

Visualization

comp_eli_maineffect <- effect("eli_self_pmc:itt_comp_gmc",
                         xlevels = list(itt_comp_gmc = c(-1.07, 0, 1.07)),
                         mod = comp_eli_randslopes)

comp_eli_maineffect <- as.data.frame(comp_eli_maineffect)
comp_eli_maineffect$itt_comp_gmc <- as.factor(comp_eli_maineffect$itt_comp_gmc)

ggplot(comp_eli_maineffect, aes(eli_self_pmc, fit, group = itt_comp_gmc)) +
  geom_smooth(method = "lm", 
                size = .7, 
                se = FALSE,
                colour = "black", 
                aes(linetype = itt_comp_gmc)) +
    theme_minimal(base_size = 13) +
    theme(legend.key.size = unit(1, "cm")) +
  scale_linetype_manual("Target-level threat",
                        breaks = c(-1.07, 0, 1.07), 
                       labels = c("Low",
                                  "Average",
                                  "High"),
                       values = c("solid",
                                  "dashed",
                                  "dotted")) +
    labs(x = "ELI responses for self",
       y = "ELI responses for target")

Assumptions

# checking normality of conditional residuals
qqnorm(residuals(comp_eli_randslopes), main="Q-Q plot for conditional residuals")

# checking the normality of the random effects (here random intercept):
qqnorm(ranef(comp_eli_randslopes)$sub_id$eli_self_pmc,
       main="Q-Q plot for the self random effect")

plot_model(comp_eli_randslopes, type='diag')

## [[1]]

## 
## [[2]]
## [[2]]$sub_id

## 
## 
## [[3]]

## 
## [[4]]

Also seems evenly spread but diagonal

Target variable

cond_eli_randslopes <- lmer(eli_targ_pmc ~ eli_self_pmc*target_condition + # itt does not work as a RE; model does not converge
                     (0 + eli_self_pmc | sub_id), 
                   data = eli_data) # Same as above, works with clean_data but not the smaller df specific to this analysis


summary(cond_eli_randslopes)

## Linear mixed model fit by REML ['lmerMod']
## Formula: eli_targ_pmc ~ eli_self_pmc * target_condition + (0 + eli_self_pmc |  
##     sub_id)
##    Data: eli_data
## 
## REML criterion at convergence: 12232.6
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -3.2042 -0.6027  0.0235  0.6548  3.1413 
## 
## Random effects:
##  Groups   Name         Variance Std.Dev.
##  sub_id   eli_self_pmc 0.03621  0.1903  
##  Residual              0.99469  0.9973  
## Number of obs: 4240, groups:  sub_id, 424
## 
## Fixed effects:
##                                                   Estimate
## (Intercept)                       -0.000000000000000003719
## eli_self_pmc                       0.137220932631810288438
## target_conditionLOSS               0.000000000000000008909
## target_conditionWARM               0.000000000000000019245
## eli_self_pmc:target_conditionLOSS -0.242898226881491041684
## eli_self_pmc:target_conditionWARM -0.150822064992466559064
##                                                 Std. Error t value
## (Intercept)                        0.025665826389154600129   0.000
## eli_self_pmc                       0.025726227692130149149   5.334
## target_conditionLOSS               0.037892422327729401166   0.000
## target_conditionWARM               0.036670523227181700543   0.000
## eli_self_pmc:target_conditionLOSS  0.037882423473722962037  -6.412
## eli_self_pmc:target_conditionWARM  0.036775376150086649951  -4.101
## 
## Correlation of Fixed Effects:
##             (Intr) el_sl_ t_LOSS t_WARM e__:_L
## eli_slf_pmc  0.000                            
## trgt_cnLOSS -0.677  0.000                     
## trgt_cnWARM -0.700  0.000  0.474              
## el_s_:_LOSS  0.000 -0.679  0.000  0.000       
## el_s_:_WARM  0.000 -0.700  0.000  0.000  0.475

tab_model(cond_eli_randslopes,
          digits = 3)

	eli_targ_pmc
Predictors	Estimates	CI	p
(Intercept)	-0.000	-0.050 – 0.050	1.000
eli self pmc	0.137	0.087 – 0.188	<0.001
target condition [LOSS]	0.000	-0.074 – 0.074	1.000
target condition [WARM]	0.000	-0.072 – 0.072	1.000
eli self pmc * target condition [LOSS]	-0.243	-0.317 – -0.169	<0.001
eli self pmc * target condition [WARM]	-0.151	-0.223 – -0.079	<0.001
Random Effects
σ2	0.99
τ00
τ00
τ11 sub_id.eli_self_pmc	0.04
ρ01
ρ01
ICC	0.06
N sub_id	424
Observations	4240
Marginal R2 / Conditional R2	0.016 / 0.072

Simple Slopes

targ_levels <-list(target_condition = c("CONTROL", "LOSS", "WARM"))
simpslopes_eli_nostereo_cond <- emtrends(cond_eli_randslopes, ~ target_condition,
                              var ="eli_self_pmc",
                              at = targ_levels)


simpslopes_eli_nostereo_cond 

##  target_condition eli_self_pmc.trend     SE  df asymp.LCL asymp.UCL
##  CONTROL                      0.1372 0.0257 Inf    0.0868    0.1876
##  LOSS                        -0.1057 0.0278 Inf   -0.1602   -0.0512
##  WARM                        -0.0136 0.0263 Inf   -0.0651    0.0379
## 
## Degrees-of-freedom method: asymptotic 
## Confidence level used: 0.95

pairs(simpslopes_eli_nostereo_cond)

##  contrast       estimate     SE  df z.ratio p.value
##  CONTROL - LOSS   0.2429 0.0379 Inf   6.412  <.0001
##  CONTROL - WARM   0.1508 0.0368 Inf   4.101  0.0001
##  LOSS - WARM     -0.0921 0.0383 Inf  -2.407  0.0426
## 
## Degrees-of-freedom method: asymptotic 
## P value adjustment: tukey method for comparing a family of 3 estimates

test(simpslopes_eli_nostereo_cond)

##  target_condition eli_self_pmc.trend     SE  df z.ratio p.value
##  CONTROL                      0.1372 0.0257 Inf   5.334  <.0001
##  LOSS                        -0.1057 0.0278 Inf  -3.800  0.0001
##  WARM                        -0.0136 0.0263 Inf  -0.518  0.6048
## 
## Degrees-of-freedom method: asymptotic

Assumptions

# checking normality of conditional residuals
qqnorm(residuals(cond_eli_randslopes), main="Q-Q plot for conditional residuals")

# checking the normality of the random effects
qqnorm(ranef(cond_eli_randslopes)$sub_id$eli_self_pmc,
       main="Q-Q plot for the self random effect")

plot_model(cond_eli_randslopes, type='diag')

## [[1]]

## 
## [[2]]
## [[2]]$sub_id

## 
## 
## [[3]]

## 
## [[4]]

Heavy tail?

Also seems evenly spread but diagonal

Visualization

eli_data %<>% 
  mutate(target_condition = forcats::fct_relevel(target_condition, c("CONTROL", "WARM", "LOSS")))

target_labels <- c("CONTROL" = "Control target",
                   "WARM" = "Warm target",
                   "LOSS" = "Loss target")

eli_cond_df <- effect("eli_self_pmc:target_condition",
                         xlevels = list(target_condition = c("CONTROL",
                                                             "WARM",
                                                             "LOSS")),
                         mod = cond_eli_randslopes)

eli_cond_df <- as.data.frame(eli_cond_df)
eli_cond_df$target_condition <- as.factor(eli_cond_df$target_condition)

ggplot(eli_cond_df, aes(eli_self_pmc, fit, group = target_condition)) +
  geom_smooth(method = "lm", 
                size = .7, 
                se = FALSE,
                colour = "black", 
                aes(linetype = target_condition)) +
    theme_minimal(base_size = 13) +
    theme(legend.key.size = unit(1, "cm")) +
  scale_linetype_manual("Target Variable",
                        breaks = c("CONTROL", "WARM", "LOSS"), 
                       labels = c("Least threatening",
                                  "Medium threatening",
                                  "High threatening"),
                       values = c("solid",
                                  "dashed",
                                  "dotted")) 

    labs(x = "ELI responses for self",
       y = "ELI responses for target")

## $x
## [1] "ELI responses for self"
## 
## $y
## [1] "ELI responses for target"
## 
## attr(,"class")
## [1] "labels"

Analog x threat composite

analogcomp_eli_randslopes <- lmer(eli_targ ~ eli_self_pmc*analog_condition*itt_comp_gmc +
       (0 + eli_self_pmc | sub_id), data = eli_data)
summary(analogcomp_eli_randslopes)

## Linear mixed model fit by REML ['lmerMod']
## Formula: eli_targ ~ eli_self_pmc * analog_condition * itt_comp_gmc + (0 +  
##     eli_self_pmc | sub_id)
##    Data: eli_data
## 
## REML criterion at convergence: 12722.4
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.51750 -0.68352 -0.07376  0.76725  2.57997 
## 
## Random effects:
##  Groups   Name         Variance Std.Dev.
##  sub_id   eli_self_pmc 0.0289   0.170   
##  Residual              1.1260   1.061   
## Number of obs: 4240, groups:  sub_id, 424
## 
## Fixed effects:
##                                                    Estimate Std. Error t value
## (Intercept)                                        3.127608   0.023557 132.767
## eli_self_pmc                                       0.004498   0.022279   0.202
## analog_conditioncontrol                            0.035595   0.032696   1.089
## itt_comp_gmc                                      -0.118886   0.022344  -5.321
## eli_self_pmc:analog_conditioncontrol               0.020146   0.030791   0.654
## eli_self_pmc:itt_comp_gmc                         -0.059057   0.020877  -2.829
## analog_conditioncontrol:itt_comp_gmc               0.042211   0.030584   1.380
## eli_self_pmc:analog_conditioncontrol:itt_comp_gmc -0.051639   0.028680  -1.801
## 
## Correlation of Fixed Effects:
##             (Intr) el_sl_ anlg_c itt_c_ el__:_ e__:__ an_:__
## eli_slf_pmc  0.000                                          
## anlg_cndtnc -0.721  0.000                                   
## itt_cmp_gmc  0.073  0.000 -0.053                            
## el_slf_pm:_  0.000 -0.724  0.000  0.000                     
## el_slf_p:__  0.000  0.047  0.000  0.000 -0.034              
## anlg_cnd:__ -0.053  0.000  0.007 -0.731  0.000  0.000       
## el_sl_:_:__  0.000 -0.034  0.000  0.000 -0.012 -0.728  0.000

tab_model(analogcomp_eli_randslopes)

	eli_targ
Predictors	Estimates	CI	p
(Intercept)	3.13	3.08 – 3.17	<0.001
eli self pmc	0.00	-0.04 – 0.05	0.840
analog condition [control]	0.04	-0.03 – 0.10	0.276
itt comp gmc	-0.12	-0.16 – -0.08	<0.001
eli self pmc * analog condition [control]	0.02	-0.04 – 0.08	0.513
eli self pmc * itt comp gmc	-0.06	-0.10 – -0.02	0.005
analog condition [control] * itt comp gmc	0.04	-0.02 – 0.10	0.168
(eli self pmc * analog condition [control]) * itt comp gmc	-0.05	-0.11 – 0.00	0.072
Random Effects
σ2	1.13
τ00
τ00
τ11 sub_id.eli_self_pmc	0.03
ρ01
ρ01
ICC	0.04
N sub_id	424
Observations	4240
Marginal R2 / Conditional R2	0.022 / 0.063

Analog x target variable

analogcond_eli_randslopes <- lmer(eli_targ ~ eli_self_pmc*analog_condition*target_condition +
       (0 + eli_self_pmc | sub_id), data = eli_data)
summary(analogcond_eli_randslopes)

## Linear mixed model fit by REML ['lmerMod']
## Formula: eli_targ ~ eli_self_pmc * analog_condition * target_condition +  
##     (0 + eli_self_pmc | sub_id)
##    Data: eli_data
## 
## REML criterion at convergence: 12695.5
## 
## Scaled residuals: 
##      Min       1Q   Median       3Q      Max 
## -2.46976 -0.62515 -0.04895  0.75378  2.64903 
## 
## Random effects:
##  Groups   Name         Variance Std.Dev.
##  sub_id   eli_self_pmc 0.03014  0.1736  
##  Residual              1.11583  1.0563  
## Number of obs: 4240, groups:  sub_id, 424
## 
## Fixed effects:
##                                                             Estimate Std. Error
## (Intercept)                                                3.3126761  0.0396434
## eli_self_pmc                                               0.1419875  0.0380866
## analog_conditioncontrol                                   -0.0226761  0.0544646
## target_conditionWARM                                      -0.2010819  0.0564690
## target_conditionLOSS                                      -0.3439261  0.0575768
## eli_self_pmc:analog_conditioncontrol                      -0.0092576  0.0518635
## eli_self_pmc:target_conditionWARM                         -0.1654422  0.0538018
## eli_self_pmc:target_conditionLOSS                         -0.2487041  0.0552807
## analog_conditioncontrol:target_conditionWARM               0.1084503  0.0777930
## analog_conditioncontrol:target_conditionLOSS              -0.0007614  0.0803329
## eli_self_pmc:analog_conditioncontrol:target_conditionWARM  0.0266920  0.0740320
## eli_self_pmc:analog_conditioncontrol:target_conditionLOSS  0.0120479  0.0762011
##                                                           t value
## (Intercept)                                                83.562
## eli_self_pmc                                                3.728
## analog_conditioncontrol                                    -0.416
## target_conditionWARM                                       -3.561
## target_conditionLOSS                                       -5.973
## eli_self_pmc:analog_conditioncontrol                       -0.178
## eli_self_pmc:target_conditionWARM                          -3.075
## eli_self_pmc:target_conditionLOSS                          -4.499
## analog_conditioncontrol:target_conditionWARM                1.394
## analog_conditioncontrol:target_conditionLOSS               -0.009
## eli_self_pmc:analog_conditioncontrol:target_conditionWARM   0.361
## eli_self_pmc:analog_conditioncontrol:target_conditionLOSS   0.158
## 
## Correlation of Fixed Effects:
##             (Intr) el_sl_ anlg_c t_WARM t_LOSS el__:_ e__:_W e__:_L a_:_WA
## eli_slf_pmc  0.000                                                        
## anlg_cndtnc -0.728  0.000                                                 
## trgt_cnWARM -0.702  0.000  0.511                                          
## trgt_cnLOSS -0.689  0.000  0.501  0.483                                   
## el_slf_pm:_  0.000 -0.734  0.000  0.000  0.000                            
## el_s_:_WARM  0.000 -0.708  0.000  0.000  0.000  0.520                     
## el_s_:_LOSS  0.000 -0.689  0.000  0.000  0.000  0.506  0.488              
## anlg_:_WARM  0.510  0.000 -0.700 -0.726 -0.351  0.000  0.000  0.000       
## anlg_:_LOSS  0.493  0.000 -0.678 -0.346 -0.717  0.000  0.000  0.000  0.475
## e__:_:_WARM  0.000  0.514  0.000  0.000  0.000 -0.701 -0.727 -0.354  0.000
## e__:_:_LOSS  0.000  0.500  0.000  0.000  0.000 -0.681 -0.354 -0.725  0.000
##             a_:_LO e__:_:_W
## eli_slf_pmc                
## anlg_cndtnc                
## trgt_cnWARM                
## trgt_cnLOSS                
## el_slf_pm:_                
## el_s_:_WARM                
## el_s_:_LOSS                
## anlg_:_WARM                
## anlg_:_LOSS                
## e__:_:_WARM  0.000         
## e__:_:_LOSS  0.000  0.477

tab_model(analogcond_eli_randslopes)

	eli_targ
Predictors	Estimates	CI	p
(Intercept)	3.31	3.23 – 3.39	<0.001
eli self pmc	0.14	0.07 – 0.22	<0.001
analog condition [control]	-0.02	-0.13 – 0.08	0.677
target condition [WARM]	-0.20	-0.31 – -0.09	<0.001
target condition [LOSS]	-0.34	-0.46 – -0.23	<0.001
eli self pmc * analog condition [control]	-0.01	-0.11 – 0.09	0.858
eli self pmc * target condition [WARM]	-0.17	-0.27 – -0.06	0.002
eli self pmc * target condition [LOSS]	-0.25	-0.36 – -0.14	<0.001
analog condition [control] * target condition [WARM]	0.11	-0.04 – 0.26	0.163
analog condition [control] * target condition [LOSS]	-0.00	-0.16 – 0.16	0.992
(eli self pmc * analog condition [control]) * target condition [WARM]	0.03	-0.12 – 0.17	0.718
(eli self pmc * analog condition [control]) * target condition [LOSS]	0.01	-0.14 – 0.16	0.874
Random Effects
σ2	1.12
τ00
τ00
τ11 sub_id.eli_self_pmc	0.03
ρ01
ρ01
ICC	0.04
N sub_id	424
Observations	4240
Marginal R2 / Conditional R2	0.031 / 0.072

Correlation matrix (multicolinearity)

cor_predictors_eli <- clean_data_eli %>% 
  select(sub_id, eli_number, eli_self, eli_targ, itt_comp) %>% 
  unique() %>% 
  na.omit() %>% 
  select(eli_self, eli_targ, itt_comp) %>% 
  rename("ELI: Self" = eli_self,
         "ELI: Target" = eli_targ,
         "Threat Composite" = itt_comp)

cor_matrix_predictors_eli <- cor(cor_predictors_eli)

corrplot(cor_matrix_predictors_eli, 
         is.corr = TRUE, 
         #method = "number", 
         method = 'color',
         tl.cex = .85,
         tl.col = 'black',
         addgrid.col = 'white',
         addCoef.col = 'grey50',
         type = 'lower')